Problem

Source: Sharygin 2023 - P16 (Grade-9-11)

Tags: geometry, reflection, altitudes, Sharygin Geometry Olympiad, Sharygin 2023



Let AHA and BHB be the altitudes of a triangle ABC. The line HAHB meets the circumcircle of ABC at points P and Q. Let A be the reflection of A about BC, and B be the reflection of B about CA. Prove that A,B,P,Q are concyclic.